Latest TCS Aptitude Question SOLUTION: In how many ways can 20 identical pencils be distributed among three girls so that each gets at least 1 pencil?

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In how many ways can 20 identical pencils be distributed among three girls so
that each gets at least 1 pencil?

Asked In TCS nagraj (11 years ago)

Unsolved Read Solution (8)

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Read Solution (8) :

Garima  (11 years ago)

consider 3 girls as A,B,C THEN A+B+C=20, but each one should get atleast 1 pencil so giving 1 pencil to each student,
the remaining pencils are 20-3=17
now A'+B'+C''=17,
number of non negative integers of A',B',C' are (17+3-1)C(3-1)

so total Combinations are 19c2=19*9 = 171,

Is this solution Helpfull? Yes (24) | No (3)  

Kiran Datti  (11 years ago)

simple formula for this kind of problems is

(n-1)c(r-1)

so 19c2= 171

Is this solution Helpfull? Yes (24) | No (1)  

Priyabrat Padhy  (11 years ago)

Garima Nice answer Can u please explain solution for previous question??

Is this solution Helpfull? Yes (3) | No (5)  

Priyabrat Padhy  (11 years ago)

171 is Correct answer. 19C2=171

Is this solution Helpfull? Yes (1) | No (4)  

SHANU MAHAJAN  (11 years ago)

GARIMA CAN U PLS EXPLAIN ME THE LOGIC BEHIND (17+3-1)C(3-1) CALCULATION

Is this solution Helpfull? Yes (1) | No (1)  

Nobinaads  (11 years ago)

plz explain it.....

Is this solution Helpfull? Yes (1) | No (1)  

surya pratap  (11 years ago)

what if each girl gets at least 2 pencils then what would have been the solution considering your formula (n-1)C(r-1)

Is this solution Helpfull? Yes (1) | No   

shubham srivastav  (11 years ago)

The first girl can take from 1 to 18 pencils. If she takes 1, the second girl can take
from 1 to 18. If she takes 2, the second girl can take from 1 to 17, and so on. The
third girl simply takes whatever is left. Hence the total number of ways is
18+17+…+1=(18*19)/2 =171.

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